Does torque normally change with battery voltage?

The title says it all. I have a gazelle Innergy 36V e-bike with a geared front hub motor.
I only have to commute 3km to work, but there is a rather steep slope of a few hundred meters.
That's where I get the impression that the motor pulls much harder with a full battery compared to when the battery voltage is lower.
A full battery can give up to 41.5V bringing cable losses and internal battery resistance into the equation, let's assume we have 40V arriving at the motor under load.
A nearly empty battery might only still give 30V to the motor. That's like 25% less.
However, the theory says that voltage is important for maximum speed and current for torque.
On the other hand, if I feed the motor with 40V and 8A it will get 320W. If I feed only 30V and 8A, it's 240W
I searched the internet but couldn't find if this behavour is normal.
Maybe some controllers increase motor current when the voltage get's lower, maintaining the legal allowed mean power going to the motor?
Mid drive motors likely will have a different behavour, as you will switch to a lower gear when climbing.
The gazelle Innergy has the motor controller build in the motor. It uses a TI DSP microcontroller, so there isn't much room for experimentation. I was playing with the idea of using a boost converter or maybe adding 2S in serie with the battery and using a step down on them to keep the battery always full. (as a matter of speech)

Welcome to ES.

Yes torque often changes with battery voltage, not directly but due to consequences. It is Normal.

Torque is (directly proportional to) motor current. Max motor current is from (battery voltage minus back EMF) divided by system resistance. Back EMF is proportional to speed (and motor Kv that is fixed).

When the battery voltage falls off there just isn't as much "pressure" to drive the motor current through the system resistance.

Controller limits can reduce duty cycle to limit battery current, speed, power, or motor current. They commonly do all of these to protect the battery and motor, and regulate to meet local laws.

Moving to 48 volts makes a "huge" difference, but may require a different controller. 36 volt ebikes don't have a lot to work with. Being able to change controller parameters is very useful.

Some have used boost converters to increase voltage. Might work here to keep at max voltage. Increasing battery capacity would help, especially using LiFePO4 with flatter discharge curve (much less "sag").

obcd said:

The title says it all. I have a gazelle Innergy 36V e-bike with a geared front hub motor.
I only have to commute 3km to work, but there is a rather steep slope of a few hundred meters.
That's where I get the impression that the motor pulls much harder with a full battery compared to when the battery voltage is lower.
A full battery can give up to 41.5V bringing cable losses and internal battery resistance into the equation, let's assume we have 40V arriving at the motor under load.
A nearly empty battery might only still give 30V to the motor. That's like 25% less.
However, the theory says that voltage is important for maximum speed and current for torque.
On the other hand, if I feed the motor with 40V and 8A it will get 320W. If I feed only 30V and 8A, it's 240W
I searched the internet but couldn't find if this behavour is normal.
Maybe some controllers increase motor current when the voltage get's lower, maintaining the legal allowed mean power going to the motor?
Mid drive motors likely will have a different behavour, as you will switch to a lower gear when climbing.
The gazelle Innergy has the motor controller build in the motor. It uses a TI DSP microcontroller, so there isn't much room for experimentation. I was playing with the idea of using a boost converter or maybe adding 2S in serie with the battery and using a step down on them to keep the battery always full. (as a matter of speech)

Click to expand...

Voltage sag means higher amps required just to get the same power.

Keep the voltage higher, get your power at lower amps, less stress, more efficient less waste as heat

john61ct said:

Voltage sag means higher amps required just to get the same power.

Keep the voltage higher, get your power at lower amps, less stress, more efficient less waste as heat

Click to expand...

Raising battery voltage lowers battery current for the same power. However motor voltage/current don't change for same power. Controller is effectively a buck converter from battery to motor. Stress is not changed significantly.

Alan B said:

john61ct said:

Voltage sag means higher amps required just to get the same power.

Keep the voltage higher, get your power at lower amps, less stress, more efficient less waste as heat

Click to expand...

Raising battery voltage lowers battery current for the same power. However motor voltage/current don't change for same power. Controller is effectively a buck converter from battery to motor.

Click to expand...

So you mean, the only way to get more torque from a higher input voltage (battery)

is to rewind the motor to a lower kV?

I see 2 possible options to always get the maximam possible torque.

1. Use a boost converter so that the motor always get's 40V. This has the disadvantage that the current drawn from the battery will increase. If we consider The 40V * 8A example, that's 320W Assume the converter efficency is 90%, than we have another 32W that goes up in heat. This brings the total needed power to 352W. Such a power would draw 11,35A from the battery.
The gazelle Innergy batteries has an intellegent BMS that has a buildin current measuring shunt resistor.
So it wouldn't suprise me that the battery will turn off if 2 much current is drawn from it.

2. Add an additional small 2S 4P battery to the system. This should be able to boost the battery voltage with 6.2 - 8.2V (depending upon the condition of that battery). A buildin step down converter should decrease that voltage when needed to prevent going over 41.5V motor voltage. The disadvantage of such a system is that the smaller battery needs to be charged as well and will need it's own BMS.
Makes me wonder, why doesn't those solutions already exist (or aren't they used)?
Maybe most motors have enough torque, even when the battery runs on it's last legs?

john61ct said:

Alan B said:

john61ct said:

Voltage sag means higher amps required just to get the same power.

Keep the voltage higher, get your power at lower amps, less stress, more efficient less waste as heat

Click to expand...

Raising battery voltage lowers battery current for the same power. However motor voltage/current don't change for same power. Controller is effectively a buck converter from battery to motor.

Click to expand...

So you mean, the only way to get more torque from a higher input voltage (battery)

is to rewind the motor to a lower kV?

Click to expand...

No. The key here is "at the same power". The way to get more torque is to increase the motor current. Higher voltage allows forcing more current into the motor. The power will not be the same.

obcd said:

I see 2 possible options to always get the maximam possible torque.

1. Use a boost converter so that the motor always get's 40V. This has the disadvantage that the current drawn from the battery will increase. If we consider The 40V * 8A example, that's 320W Assume the converter efficency is 90%, than we have another 32W that goes up in heat. This brings the total needed power to 352W. Such a power would draw 11,35A from the battery.
The gazelle Innergy batteries has an intellegent BMS that has a buildin current measuring shunt resistor.
So it wouldn't suprise me that the battery will turn off if 2 much current is drawn from it.

2. Add an additional small 2S 4P battery to the system. This should be able to boost the battery voltage with 6.2 - 8.2V (depending upon the condition of that battery). A buildin step down converter should decrease that voltage when needed to prevent going over 41.5V motor voltage. The disadvantage of such a system is that the smaller battery needs to be charged as well and will need it's own BMS.
Makes me wonder, why doesn't those solutions already exist (or aren't they used)?
Maybe most motors have enough torque, even when the battery runs on it's last legs?

Click to expand...

The simplest solutions are generally the best. Using a sufficiently high voltage battery so the sag doesn't reduce the torque too much. The controller can be set up to deliver reduced torque at the full charge cycle and thus create level torque across the cycle.

Another solution is to pedal harder.

Most ebike makers are just concerned with making a profit rather than having any particular amount of torque at the end of the battery capacity.

We had a similar issue with my son's commuter ebike. So we changed the controller. It already has a 48V battery, the controller is the main limiting factor. Many folks have bypassed the in-motor controllers as they are generally quite limited.

The torque produced is directly related to watts fed to the motor, and the limit is the motor saturation.

Higher voltage does mean more watts, given equal Amps so yes, it will produce more torque but it will also spin faster. Good if you use that extra speed, but a handicap in efficiency if you keep riding the same speed. Then some of the extra watts will be lost in heat.

Big Amps are the way to make big torque, while voltage should be adjusted to do most of the ride in the motor efficient RPM zone. So, high C rate battery (or big battery) is the first thing you need for serious power, and next a controller that can feed as much as the motor can take.

Warning: Building for torque does require conscious heat monitoring, means of limiting resistance, and means to shed the heat that you can’t help limiting production.

I am searching for solutions using the stuff I have. The front fork is wider than most normal bike forks, so finding a replacement motor isn't easy.
The system has a torque / pas sensor, and I like the way it works with that.
The cabling is also nicely integrated in the frame.
My next ebike likely will have the Tungsheng TDSZ2 mid drive motor.
I got the current bike second hand with 2 batteries, so I might use that second battery with the TDSZ2 motor.
I know a bit of electronics, but bike mechanichs isn't my expertise.
I got a third bad battery cheap and hope I can recover some of the cells of that to make my 2S battery.

Thanks so far for all the answers / suggestions.

The simplest solution is to avoid using the end of the battery capacity where sag becomes a factor. Increase the capacity of the battery by paralleling additional cells. They can be tied in so the BMS, charging, etc remains the same.

The torque produced is directly related to watts fed to the motor, and the limit is the motor saturation.

Click to expand...

That's not a good way to think about it, IMO. Increasing total watts does not necessarily you are increasing peak torque output. It can.. but not always.

I am probably butchering some of the terminology, but...

A more accurate way of thinking about things is that torque output is a function of the amount of amperage flowing through the motor windings. More current = stronger magnets = stronger torque. This is because the strength of the electromagnets relates to the amperage flowing through it. Also the number of winding increases the effect of the amps on magnetic strength.

Also more amperage means more heat. Which is why when the motor is producing peak torque it's also really inefficient.

When determining magnetic strength through measuring electricity you can ignore total wattage and volts and just worry about measuring the amount of amps actually flowing.


Now there are a variety of ways to increase amperage so that you can increase torque. Which method you use depends on what is limiting the current flowing.

So say you want to increase top speed:

If you want to increase the top speed of the bike you need to increase the torque at high rpms so you can overcome wind resistance and rolling resistance. Since at high RPMs the limitation on current is ability of the battery voltage to overcome 'back EMF voltage' increasing the voltage will allow more amperage to flow at those higher rpms. Which allows you to go faster.

Now say you want to increase amperage at very low RPMs to help with acceleration off the line:

At low RPM you are probably limited by the phase amperage limits in the controller. If you are bumping up against phase current limits then increasing voltage won't increase torque output. You have to figure out a way to increase those amperage limits.


Now wattage is POWER. It's measuring energy (jules) per second. It's the same thing that horsepower measures in this instance. When it comes to motor output wattage is torque over time. Torque does not have a time element, it's more of a absolute value. Torque tells you the force of a wheel spinning, but it doesn't tell you the rate at which it is happening. Rate-at-which-something-happens is what we care about performance, so converting torque to wattage using RPMs is a important measurement.

Power (kW) = Torque (N.m) x Speed (RPM) / 9.5488


Here is a simulation showing the effect of voltage on torque:

https://www.ebikes.ca/tools/simulator.html?bopen=true&batt_b=B7223_AC&axis=rpm&grade_b=0&grade=0&hp=0&hp_b=0&cont=C20&cont_b=C20

Same motor, same controller limits, only thing that is different is the voltage.

The blue line is torque output. Notice that the 36v motor has same peak torque output as the 72v motor... 45nm. But the 72v motor is able to move those torque limits much higher in the RPM range. Which is why we would get so much more power and performance out of a 72v version of that motor.

Lots of good info here, but the motors are the same (as was mentioned). So referring to one as a 36V motor and the other as a 72V motor is confusing. Might be better to edit it and call it the 36V system vs the 72V system. And you can get more performance out of the same motor with a 72V system...

The original poster is getting adequate performance with the fully charged battery and inadequate performance with a sagging battery later in the discharge, and he doesn't want to change much in his system. I wonder what the controller will actually accept in terms of voltage?

Great summary to this noobs eyes, I hope the expert will correct / clarify anything there that isn't just right.

sleepy_tired said:

But the 72v motor is able to move those torque limits much higher in the RPM range. Which is why we would get so much more power and performance out of a 72v version of that motor.

Click to expand...

But **only** if speed is part of the issues being solved, right?

taking gearing out of the picture

If "torque alone" at lower speeds/rpm is the only issue.

starting off the line

going up long steep inclines

carrying very heavy loads

and especially, all three together,

then going to higher **battery** input voltage to the controller helps nothing,

is that correct?

Apparently changing the winding / kV of the motor also doesn't help?

Elsewhere, I was categorically told that

**only** the ability to abide / use high phase amps, which means tolerating / shedding heat, will help,

IOW, the physical size of the motor, the mass of its internal stator steel (iron?), copper windings and size of the magnets **alone** determines the torque available at low rpm

I don't see how increasing the motor (phase) voltage helps, or even how that would be done

This thread started with an observation about reduced torque due to battery sag. Clearly that is an example of this.

There are many ways to think about these electromechanical systems. Some of them lend themselves to understanding more than others.

The back EMF of the motor fights the battery voltage and limits the current that can be forced into the motor. Using higher voltage overcomes the back EMF and allows the controller to push more current into the motor.

If the bike goes 25 on the level, and you want to go uphill at 20 the back EMF will limit the torque. If you have more voltage you can force more current into the motor and get the low speed torque back. If you don't have extra voltage the torque falls off as the motor speeds up, it is not constant. Even if you never plan to go more than 20 you need more voltage than it takes to go 20, otherwise you will have very little torque available to overcome wind or gradients at 20 and you will fall back to lower speed on every hill.

As to whether the motor melts, that is mostly a function of I squared R which is heat in the motor. Torque is proportional to I, up to saturation. But saturation is not a wall. Beyond the first knee the torque still goes up with current, but at a lesser rate. Of course heat is going up with current squared, so you don't want to operate there for long. So it is a balance between motor dissipation capacity and thermal mass and length of the climb and speed. If you force too much current into the motor it will start heating up, will you get to the top before it overheats?

At very low speeds battery voltage is not much of a problem because back EMF is very low so full torque can be generated. As speed rises the ability to generate the same torque falls off due to back EMF.

What they told you isn't wrong, it is just part of the whole picture.

OK thanks, getting clearer, and yes my scenario is only for very low speeds, bottom end of what the motor supports.

It's not like I want to climb that hill at 25km/hr.

So, if back EMF limitting the current isn't the issue reducing torque, there has to be something else on my bike reducing the current at lower battery voltage.
If I read all comments correctly, there is no electrical limitation that explains such behavour.

I noticed in the dealer software that there is a flag called "accu compensation" Maybe it's related to the problem, but I am not having that software. (Just a few pdf's describing some options)

Yes, anytime the volts is less, the total wattage the controller can offer the motor is less. Less watts means the motor's maximum torque possible is less.

Actual torque is affected by a lot of complicated stuff, as talked about above. But in your case, its just a steep hill, and your system is not high powered. So it will struggle to get up it. But you still get about the same help as a second guy pedaling with you right now. That's not bad.

What is most likely happening to you is a lot of your wattage is turning into heat as you climb that hill. You slow down, efficiency drops, and you start putting in 350w but 200 w is making heat. You might be losing 50w to lower voltage, but you are losing most of it to overloading the motor, making it make excess heat.

But dude, your ride is really short. Too short to melt your motor. Even on the way back, you are not on an empty battery. But yes, start out full, so you have the most you can get. You are getting there, you have help, and the ride is too short to sweat too much.

Just pedal a bit harder to get up that hill. It cant be that long, your whole ride is 3 km. Your commute is easy. Mine, it had a 1000 foot tall hill, half way along a 15 mile ride. I needed 48v systems to effectively get up that monster.

You would like more, I'm sure, and will likely spend more to get it later. But right now, you seriously risk overvolting your system if you add 8v to it on a ride that short. Most likely your system will just shut down if it gets 48v, or fry if it gets more than 50v.

One last thing though,, what do you weigh? if its 300 pounds,, then your bike will never have the power it needs to climb a steep hill with a load that big. The smaller motors are designed for riders less than 200 pounds. For a really heavy rider, a mid drive is the type to choose. A mid drive can gear down, and keep the motor rpm up. As a general rule, anything less than 15 mph up a hill with a hub motor is making a LOT of heat, instead of torque. A mid drive can grind up a hill at 5 mph, and in the right gear, keep the motor rpm high, and efficient.

obcd said:

It's not like I want to climb that hill at 25km/hr.

So, if back EMF limitting the current isn't the issue reducing torque, there has to be something else on my bike reducing the current at lower battery voltage.
If I read all comments correctly, there is no electrical limitation that explains such behavour.

I noticed in the dealer software that there is a flag called "accu compensation" Maybe it's related to the problem, but I am not having that software. (Just a few pdf's describing some options)

Click to expand...

I think in your case it is the combination of battery sag, speed and back EMF that reduces the available torque for you. Is there anything else other than battery state of charge between the two scenarios?

With 36V the voltage is already quite low, so the system is more sensitive to state of charge voltage sag.

Let's look at back EMF for a moment. At top speed, back EMF rises and limits the torque until there is insufficient torque to go any faster. It is a balance.

At half speed the back EMF is half as much and limits the torque to about half.

At quarter speed the back EMF limits torque to about 3/4 of full.

At zero speed the full torque is available.

So even at fairly low speeds the torque is reduced by some amount. When you are climbing this can be very noticeable and cause the speed to drop.

Note that the controller can limit torque even further but usually does this for power, current or speed limit reasons.

obcd said:

It's not like I want to climb that hill at 25km/hr.

Click to expand...

Actually, by making sure you're at least at say 10-15km/hr, then your motor will be **more** likely to get you up the hill.

It's climbing at **very low** speeds with a heavy weight that burns the motor out, faster than at a medium speed anyway.

Alan B said:

At quarter speed the back EMF limits torque to about 3/4 of full.

At zero speed the full torque is available

Click to expand...

But IRL the amps/heat issue sets a speed (voltage) floor to get the (theoretical) torque applied as (actual) work (power),

right?

If I am following, having a pack+controller (capable of in theory) reaching a higher top speed (voltage)

will allow more torque to be actually delivered by a given motor while climbing at a lower voltage/rpm.

Again, I do not care about actual speed at all, just trying to get weight up the big long hills without gearing.

You have to model your actual data to get specific useful predictions. Generalizations don't get you there, even if they are all correct for some situations.

You need enough voltage to:

1) overcome back EMF for the speed you are going and have enough voltage left to both:
2) overcome resistive losses in the battery, bms, wiring, connectors, controller and motor and
3) produce the current to generate adequate torque

You need enough motor to:

1) convert that current into torque
2) without generating too much heat

You need enough torque to:

1) overcome the air resistance for the speed
2) overcome the lifting work for the weight, gradient and speed
3) overcome various other mechanical losses

This torque producing current generates heat in the motor, primarily motor current squared times motor resistance, and you need enough motor thermal capacity and/or cooling to:

1) absorb the heat and/or
2) cool sufficiently
3) while maintaining a low enough motor temperature to survive for the duration required

It's tricky because going either too slow or too fast will increase the motor temperature, one from too much time, the other from too much current. There is an "ideal" speed which depends on the system and the hill. There may be no solution for a given combination and motor survival.

If you don't have enough voltage you are doomed to bog down and overheat.

If you have too much voltage you can throttle back a bit and be fine, going at the "optimal" speed.

If you don't have enough motor you may be doomed to overheat or fail regardless.

For these reasons people with experience tend to favor more motor and more voltage.

Or mid drives with variable gearing...

OK no time now, will parse later see if specific answers are there to see if my understanding is better.

Alan B said:

You have to model your actual data to get specific useful predictions. Generalizations don't get you there, even if they are all correct for some situations.

Click to expand...

Well when choosing and sourcing the components. . .

> Or mid drives with variable gearing...

I thought just not available big enough to push 400-500lbs up long steep mountain climbs

And yes I know, figure out the simulator

My weight is approx 230 pounds or 105 kg.
The only difference between going uphill with ease and going uphill with tough peddeling is the condition of the battery.
Obvious, the motor torque is hard to measure. Wind conditions make a difference as well. Also, one ride to work and home again is only draining the battery a little so the difference is hard to notice every ride.
I could simply charge my battery every ride, but I am reading frequently that you might get up to 3 times more charges out of your battery if you only charge it for 80 - 85%
So, if possible, I would like to avoid charging it to 100% every day. (Altough it's an option I haven't considered much yet.)
I was not going to feed my motor / controller 8V extra. I intended to give it 41V which it should handle just fine as it's what a fully charged battery is giving it as well.
Today, I tested the system in eco mode, and to my suprise, it was giving nearly the same assistance as in normal.
A closer inspection showed a fracture in the frame near the position of the torque sensor.
The frame had been welded at that position and the welding was nicely painted over to hide the repair. It's possible that the torque sensor became 2 sensitive due to the fracture. Likely the seller and maybe his service center knew about the problem and might have lowered the assistant settings a little to hide the issue.
It's a lot of conspiracy theory, I know.
Maybe the welding broke after I got the bike into my possession, and previous owner rode it happily with the welding repair and without issues. However, I don't have the impression the bike behaves any different now compared to when I first bought it.
It's a lot of questions. I might see first if the frame can be repaired and maybe fabricate something to measure my battery current.

I assume you get used to the "push in the back" real fast and simply go for the next step.

It's just a pitty you need the dealer software to check and adjust settings.

I'll post it over here if there is any progress.